1. Field of the Invention
This invention relates generally to the determination of direction means of an electromagnetic field, and more particularly to determination of direction of apparatus generating curl-free magnetic vector potential field.
2. Description of the Prior Art
It is known in the prior art to provide systems for the determination of a direction of a source generating electromagnetic fields which are solutions to Maxwell's equations. The direction determination system include apparatus for generating electromagnetic fields and apparatus for detecting the generated electromagnetic field. The generating and detecting apparatus can be made non-uniform with respect to spatial generation and detection of electromagnetic radiation fields. This non-uniformity can be used to determine a direction of a source. Examples of the prior type of direction transfer systems include microwave band systems and optical based systems.
The Maxwell equations, which govern the prior art transfer of information by electromagnetic systems can be written: ##EQU1## where E is the electric field density, H is the magnetic field intensity, B is the magnetic flux density, D is the electric displacement, J is the current density and .rho. is the change density. In this notation the bar over a quantity indicates that this is a vector quantity, i.e., a quantity for which a spatial orientatim is required for complete specification. The terms CURL, and DIV refer to the CURL and DIVERGENCE mathematical operations and are denoted symbolically by the .gradient.x and .gradient.. mathematical operations respectively. Furthermore, the magnetic field intensity and the magnetic flux density are related by the equations B=.mu.H, which the electric field density and the electric displacement are related by the equation D=.mu.H. These equations can be used to describe the transmission of electromagnetic radiation through a vacuum or through various media.
It is known in the prior art that solutions to Maxwell's equations can be obtained through the use of electric scalar potential functions and a magnetic vector potential function. The electric scalar potential is given by the expression: ##EQU2## where .phi.(1) is the scalar potential at point 1, .rho.(2) is the charge density at point 2, .sqroot.12 is the distance between point 1 and 2, and the integral is taken over all differential volumes. The magnetic vector potential is given by the expression ##EQU3## where A(1) is the vector potential at point 1, .alpha..sub.o is the permittivity of free space, C is the velocity of light J(2) is the (vector) current density at point 2. .sqroot.12 is the distance between point 1 and point 2 and the integral is taken over all differential volumes. The potential functions are related to Maxwell's equations in the following manner. ##EQU4## where GRAD is the gradient mathematical operation and is denoted symbolically by the .gradient. mathematical operator. ##EQU5## where A can contain, for completeness a term which is the gradient of a scalar function. In the remaining discussion, the scalar function will be taken to be substantially zero. Therefore, attention will be focussed on the magnetic vector potential A.
In the prior art literature, consideration has been given to the physical significance of the magnetic vector potential field A. The magnetic vector potential field was, in some instances, believed to be a mathematical artifice, useful in solving problems, but devoid of independent physical significance.
More recently, however, the magnetic vector potential has been shown to be a quantity of independent physical significance. Indeed, in quantum mechanics, the Schroedinger equation for a (non-relativistic, spinless) particle with charge q and mass m moving in an electromagnetic field is given by ##EQU6## where is Planch's constant divided by 2.pi., i is the imaginary number .degree.+1, .phi. is the electric scaler potential experienced by the particle, A is the magnetic scalar potential experienced by the particle and .psi. is the wave function of the particle. A device operating on quantum mechanical principles which can detect curl-free magnetic vector potential radiation in the Josephson junction device. It is desirable to develop a direction determination device utilizing the curl-free vector potential radiation field.